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    Frequency Response of Nonproportionally Damped, Lumped Parameter, Linear Dynamic Systems

    Source: Journal of Vibration and Acoustics:;1990:;volume( 112 ):;issue: 002::page 194
    Author:
    J. Bellos
    ,
    D. J. Inman
    DOI: 10.1115/1.2930112
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: The frequency response of nonproportionally (or nonclassically or non-Raleigh) damped linear lumped mass systems is discussed here. The exact method, via Laplace transforms, is presented and the practical difficulties revealing the necessity of approximate methods are emphasized. Modal analysis is used to transform the governing equations of motion to the respective modal coupled equations of motion. The Laplace transform is performed to transfer to the frequency domain. The modal coupling is then analyzed through coupling terms. A criterion in the form of nonproportionality indices is developed, in order to measure the extent of the modal coupling and to predict the error introduced by neglecting this coupling either partially or completely. An attempt to interpret the frequency spectrum of the modal coupling is also made. A specific application to a six degree of freedom system, with two sets of closely spaced undamped natural frequencies and moderate damping is given as an illustrative example. Useful information about the accuracy, the applicability, and the advantages of the proposed method over the exact method, as well as over the common procedure of ignoring the modal coupling, are derived.
    keyword(s): Frequency response , Linear dynamic system , Laplace transforms , Equations of motion , Degrees of freedom , Damping , Errors , Frequency AND Spectra (Spectroscopy) ,
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      Frequency Response of Nonproportionally Damped, Lumped Parameter, Linear Dynamic Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/107854
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    contributor authorJ. Bellos
    contributor authorD. J. Inman
    date accessioned2017-05-08T23:34:17Z
    date available2017-05-08T23:34:17Z
    date copyrightApril, 1990
    date issued1990
    identifier issn1048-9002
    identifier otherJVACEK-28791#194_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/107854
    description abstractThe frequency response of nonproportionally (or nonclassically or non-Raleigh) damped linear lumped mass systems is discussed here. The exact method, via Laplace transforms, is presented and the practical difficulties revealing the necessity of approximate methods are emphasized. Modal analysis is used to transform the governing equations of motion to the respective modal coupled equations of motion. The Laplace transform is performed to transfer to the frequency domain. The modal coupling is then analyzed through coupling terms. A criterion in the form of nonproportionality indices is developed, in order to measure the extent of the modal coupling and to predict the error introduced by neglecting this coupling either partially or completely. An attempt to interpret the frequency spectrum of the modal coupling is also made. A specific application to a six degree of freedom system, with two sets of closely spaced undamped natural frequencies and moderate damping is given as an illustrative example. Useful information about the accuracy, the applicability, and the advantages of the proposed method over the exact method, as well as over the common procedure of ignoring the modal coupling, are derived.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleFrequency Response of Nonproportionally Damped, Lumped Parameter, Linear Dynamic Systems
    typeJournal Paper
    journal volume112
    journal issue2
    journal titleJournal of Vibration and Acoustics
    identifier doi10.1115/1.2930112
    journal fristpage194
    journal lastpage201
    identifier eissn1528-8927
    keywordsFrequency response
    keywordsLinear dynamic system
    keywordsLaplace transforms
    keywordsEquations of motion
    keywordsDegrees of freedom
    keywordsDamping
    keywordsErrors
    keywordsFrequency AND Spectra (Spectroscopy)
    treeJournal of Vibration and Acoustics:;1990:;volume( 112 ):;issue: 002
    contenttypeFulltext
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